Problem: Simplify the following expression: ${2(7+3r)-(r+2)}$
Explanation: Distribute the ${2}$ into the first set of parentheses: $ {2(}\gray{7+3r}{)} - (r+2) $ $ {14+6r} - (r+2) $ The minus sign in front of the parentheses means we multiply each term inside the parentheses by ${-1}$ $ 14+6r {-1(}\gray{r+2}{)} $ $ 14+6r {-r-2} $ Rewrite the expression to group the ${r}$ terms and numeric terms: $ {6r - r} + {14 - 2}$ Combine the ${r}$ terms: $ {5r} + {14 - 2}$ Combine the numeric terms: $ {5r} + {12}$ The simplified expression is $5r+12$